Problem

The hyperbola $H$ has

• foci with coordinates $\left(\pm \frac{13}{2}, 0\right)$

• directrices with equations $x = \pm \frac{72}{13}$

• eccentricity $e$

Determine

(a) the value of $e$

(b) an equation for $H$, giving your answer in the form $px^2 - qy^2 = r$, where $p$, $q$ and $r$ are integers.